Non-compactness and Multiplicity Results for the Yamabe Problem on Sⁿ

Authors: Berti M.¹; Malchiodi A.²

Source: Journal of Functional Analysis, Volume 180, Number 1, February 2001 , pp. 210-241(32)

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Abstract:

The aim of this paper is to show the existence of metrics ¯g on Sⁿ, where ¯g is a perturbation of the standard metric ¯g₀, for which the Yamabe problem possesses a sequence of solutions unbounded in L(Sⁿ). The metrics ¯g that we find are of class C^k on Sⁿ with (k les n-34). We also prove some new multiplicity results. Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2–4, Trieste, 34014, Italy 2: Department of Mathematics, Hill Center, Bush Campus, Rutgers, the State University, 110 Frelinghuysen Road, Piscataway, New Jersey, 08854-8019

Publication date: 2001-02-01